Math 2210 - Assignment 10
Dylan Zwick
Fall 2008
Sections 13.6 through 13.7
1 Section 13.6
13.6.1 Find the surface area of the part of the plane 3x + 4y + 6z = 12 that
is above the rectangle in the xy-plane with vertices (0, 0), (2, 0), (2, 1),
and (0, 1). Make a sketch of the surface.
1
13.6.5 Find the surface area of the part of the cylinder x2 +z 2 = 9 that is directly over the rectangle in the xy-plane with vertices (0, 0), (2, 0), (2, 3),
and (0, 3). Make a sketch of the surface.
2
13.6.12 Find the surface area of the part of the cylinder x2 + y 2 = ay inside
the sphere x2 + y 2 + z 2 = a2 , a > 0. Hint: Project to the yz-plane to
get the region of integration. Make a sketch of the surface.
3
13.6.13 Find the surface area of the part of the saddle az = x2 − y 2 inside
the cylinder x2 + y 2 = a2 , a > 0. Make a sketch of the surface.
4
13.6.21 Four goats have grazing areas A, B, C and D, respectively. The
first three goats are each tethered by ropes of length b, the first on
a flat plane, the second on the outside of a sphere of radius a, and
the third on the inside of a sphere of radius a. The fourth goat must
stay inside a ring of radius b that has been dropped over a sphere of
radius a. Determine formulas for A, B, C and D and arrange them in
order of size. Assume that b < a.
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2 Section 13.7
13.7.1 Evaluate the iterated integral:
Z
7
−3
Z
0
2x
Z
y
6
x−1
dzdydx
13.7.5 Evaluate the iterated integral:
Z
4
24
Z
0
24−x
Z
24−x−y
0
7
y+z
dzdydx
x
13.7.10 Evaluate the iterated integral:
Z
0
π
2
Z
0
sin 2z
Z
2yz
0
8
x
sin
dxdydz
y
13.7.16 Sketch the solid:
S = {(x, y, z) : 0 ≤ x ≤ y 2 , 0 ≤ y ≤
and then write an iterated integral for:
Z Z Z
S
9
f (x, y, z)dV
√
z, 0 ≤ z ≤ 1}
13.7.22 Calculate the volume of the solid in the first octant bounded by
the elliptic cylinder y 2 + 64z 2 = 4 and the plane y = x.
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